Solve 180/x-6=120/x+6

$$\frac { 180 } { x - 6 } = \frac { 120 } { x + 6 }$$

Solve for x

$$x=-30$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,6 since division by zero is not defined. Multiply both sides of the equation by \left(x-6\right)\left(x+6\right), the least common multiple of x-6,x+6.

$$\left(x+6\right)\times 180=\left(x-6\right)\times 120$$

Use the distributive property to multiply x+6 by 180.

$$180x+1080=\left(x-6\right)\times 120$$

Use the distributive property to multiply x-6 by 120.

$$180x+1080=120x-720$$

Subtract 120x from both sides.

$$180x+1080-120x=-720$$

Combine 180x and -120x to get 60x.

$$60x+1080=-720$$

Subtract 1080 from both sides.

$$60x=-720-1080$$

Subtract 1080 from -720 to get -1800.

$$60x=-1800$$

Divide both sides by 60.

$$x=\frac{-1800}{60}$$

Divide -1800 by 60 to get -30.

$$x=-30$$